Is it ever worth trading a cannon for an elephant or advisor to break open the enemy defence?
These answers restate the rules implemented by our open-source engine, which follows the WXF laws and is regression-tested against the official 110-diagram repetition casebook. Where an answer refers to a specific position, that position lives on the linked reference page, where the build verifies it against the engine before publishing.
Direct answer
Sometimes, when that one piece is the whole defence. A cannon is worth noticeably more than an elephant or advisor in raw material terms, so this trade loses value on the exchange itself. It becomes worthwhile when the elephant or advisor being removed was the single piece blocking a mating attack, in which case the material given up is repaid many times over by what follows.
What makes the sacrifice sound
The clearest case is a lone elephant or advisor covering the one palace point your attack needs. Removing it should open an immediate, calculable follow-up, another piece delivering check or threatening mate on the very next move, rather than a vague improvement in your position.
Why it usually isn't worth it otherwise
If the defender still has other pieces covering the same square, or if your attack has no immediate follow-up ready, the trade is simply a cannon for a much cheaper piece, a bad outcome in material terms with nothing concrete to show for it. This idea is a finishing move for an attack that is already close to working, not a way to start one.
Related questions
Does this work the same way with an advisor instead of an elephant?
Yes, the logic is identical; whichever piece is the single defender of the critical point is the one worth removing.
How do I know if the follow-up is actually forced?
Calculate it out fully before playing the sacrifice, check every reasonable reply, not just the one you expect.